See also

TRandom
basic Random number generator class (periodicity = 10**8).
The following basic Random generators are provided:
===================================================
-Exp(tau)
-Integer(imax)
-Gaus(mean,sigma)
-Rndm()
-Uniform(x1)
-Landau(mean,sigma)
-Poisson(mean)
-Binomial(ntot,prob)
Random numbers distributed according to 1-d, 2-d or 3-d distributions
=====================================================================
contained in TF1, TF2 or TF3 objects.
For example, to get a random number distributed following abs(sin(x)/x)*sqrt(x)
you can do:
TF1 *f1 = new TF1("f1","abs(sin(x)/x)*sqrt(x)",0,10);
float r = f1->GetRandom();
The technique of using a TF1,2 or 3 function is very powerful.
It is also more precise than using the basic functions (except Rndm).
With a TF1 function, for example, the real integral of the function
is correctly calculated in the specified range of the function.
Getting a number from a TF1 function is also very fast.
The following table shows some timings (in microsecons/call)
for basic functions and TF1 functions.
The left column is with the compiler, the right column with CINT.
Numbers have been obtained on a Pentium 233Mhz running Linux.
g++ CINT
Rndm.............. 0.330 4.15
Gaus.............. 2.220 6.77
Landau............ 21.590 46.82
Binomial(5,0.5)... 0.890 5.34
Binomial(15,0.5).. 0.920 5.36
Poisson(3)........ 2.170 5.93
Poisson(10)....... 4.160 7.95
Poisson(70)....... 21.510 25.27
Poisson(100)...... 2.910 6.72
GausTF1........... 2.070 4.73
LandauTF1......... 2.100 4.73
Note that the time to generate a number from an arbitrary TF1 function
is independent of the complexity of the function.
For Landau distribution, it is recommended to use the TF1 technique.
TH1::FillRandom(TH1 *) or TH1::FillRandom(const char *tf1name)
==============================================================
can be used to fill an histogram (1-d, 2-d, 3-d from an existing histogram
or from an existing function.
Note this interesting feature when working with objects
=======================================================
You can use several TRandom objects, each with their "independent"
random sequence. For example, one can imagine
TRandom *eventGenerator = new TRandom();
TRandom *tracking = new TRandom();
eventGenerator can be used to generate the event kinematics.
tracking can be used to track the generated particles with random numbers
independent from eventGenerator.
This very interesting feature gives the possibility to work with simple
and very fast random number generators without worrying about
random number periodicity as it was the case with Fortran.
One can use TRandom::SetSeed to modify the seed of one generator.
a TRandom object may be written to a Root file
==============================================
-as part of another object
-or with its own key (example gRandom->Write("Random");
The small program below has been used to get the values in the table above.
#ifndef __CINT__
#include "TROOT.h"
#include "TF1.h"
#include "TRandom.h"
#include "TStopwatch.h"
void rand();
//______________________________________________________________________________
int main()
{
TROOT simple("simple","Test of random numbers");
rand();
}
#endif
void rand() {
int i, N = 1000000;
float cpn = 1000000./N;
float x;
TStopwatch sw;
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Rndm(i);
}
printf("Rndm.............. %8.3f microseconds/calln",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Gaus(0,1);
}
printf("Gaus.............. %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Landau(0,1);
}
printf("Landau............ %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Binomial(5,0.5);
}
printf("Binomial(5,0.5)... %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Binomial(15,0.5);
}
printf("Binomial(15,0.5).. %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Poisson(3);
}
printf("Poisson(3)........ %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Poisson(10);
}
printf("Poisson(10)....... %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Poisson(70);
}
printf("Poisson(70)....... %8.3fn",sw.CpuTime()*cpn);
sw.Start();
for (i=0;i<N;i++) {
x = gRandom->Poisson(100);
}
printf("Poisson(100)...... %8.3fn",sw.CpuTime()*cpn);
TF1 *f1 = new TF1("f1","gaus",-4,4);
f1->SetParameters(1,0,1);
sw.Start();
for (i=0;i<N;i++) {
x = f1->GetRandom();
}
printf("GausTF1........... %8.3fn",sw.CpuTime()*cpn);
TF1 *f2 = new TF1("f2","landau",-5,15);
f2->SetParameters(1,0,1);
sw.Start();
for (i=0;i<N;i++) {
x = f2->GetRandom();
}
printf("LandauTF1......... %8.3fn",sw.CpuTime()*cpn);
}

Generates a random integer N according to the binomial law
Coded from Los Alamos report LA-5061-MS
N is binomially distributed between 0 and ntot inclusive
with mean prob*ntot.
prob is between 0 and 1.
Note: This function should not be used when ntot is large (say >100).
The normal approximation is then recommended instead
(with mean =*ntot+0.5 and standard deviation sqrt(ntot*prob*(1-prob)).

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